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Lp(·)Lq(·) boundedness of some integral operators obtained by extrapolation techniques

  • Marta Urciuolo EMAIL logo and Lucas Vallejos

Abstract

Given a matrix A such that AM=I and 0α<n, for an exponent p satisfying p(Ax)=p(x) for a.e. xn, using extrapolation techniques, we obtain Lp()Lq() boundedness, 1q()=1p()-αn, and weak type estimates for integral operators of the form

Tαf(x)=f(y)|x-A1y|α1|x-Amy|αm𝑑y,

where A1,,Am are different powers of A such that Ai-Aj is invertible for ij, α1++αm=n-α. We give some generalizations of these results.

MSC 2010: 42B25; 42B35

Funding statement: Partially supported by CONICET and SECYTUNC.

References

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Received: 2016-10-10
Revised: 2017-01-27
Accepted: 2017-08-24
Published Online: 2018-11-14
Published in Print: 2020-09-01

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